2002 Pontiac Grand Am starting to slip

In the past several months i noticed that if my car is not warmed up the car will barely move up my hill. when i go around a very sharp corner it also hesitates and then punches into gear. i have it serviced by the dealer so i am assuming they check the transmission fluid reguarly. how to i broach the subject with some knowledge for them to check it without trying to sell me a new transmission. then again if i myself cannot check it how do i know if they are giving me a snow job by telling me i need a new transmission. If i do need one what it the going rate. I live in CT so things are usually more expensive. Thanks